Problem: Simplify the following expression: $k = \dfrac{a - 12}{3a - 7} - \dfrac{9a - 19}{3a - 7}$
Answer: Since the expressions have the same denominator we simply subtract the numerators: $k = \dfrac{a - 12 - (9a - 19)}{3a - 7}$ Distribute the negative sign: $k = \dfrac{a - 12 - 9a + 19}{3a - 7}$ Combine like terms: $k = \dfrac{-8a + 7}{3a - 7}$